The size spectrum of small Air Shower at Ooty GRAPES
III (800g/cm2).
Y.Hayashi2, Y.Aikawa2, N.Ikeda2, S.K.Gupta1, N.Ito2, S.Kawakami2, S.Miyake2, D.K.Mohanty1,M.Sasano2, K.Sivaprasad1, B.V.Sreekantan1, H.Tanaka2, K.Sasaki2 and S.C.Tonwar1
1
Tata Institute of Fundamental Research, Mumbai 400 005, INDIA
2
Faculty of Science, Osaka City University, Osaka 558 8585, JAPANABSTRACT
Our GRAPES III has started its Air Shower observation from the beginning of 1998 using
around 100 detectors out of 217 located in position. So far about 10 months data have beencollected. Total 1.6 million Air showers (about 4 months data) were used to derive the sizespectrum between 104 to 106,
We derived the energy spectrum and chemical composition of primary cosmic rays
(1014eV<E0<1016eV) from the size spectrum of the Air Showers (104< Ne < 106) at Ooty
(800g/cm2) using the semi Monte Carlo simulation code GENAS (Kasahara and Torii). Though
present work showed about 25% lower than the Proton Satellite's result in these energy range.
Considering the amount of systematic error in observed data and analysis method to derive theenergy spectrum in both experiment, we don't see serious discrepancy between those results.
INTRODUCTION
The main aim of our present work is to understand the reason of steepening in energy
spectrum around 1--3 x 1015 eV, so called knee. One possible attempt is to explain it in terms ofpropagation effects of cosmic rays in the galactic disk and their leakage from the disk due tolarger radii than galactic size and another is in terms of changes in the accelerating mechanism
in cosmic ray sources at energy around 1015-16 eV. The better resolution is required to understandthe real cause of existence of knee.
Also there are still different results among some observations about knee position andabsolute flux of primary cosmic rays. We obtained the size spectrum of Air shower at Ooty fromthe observed data and compared with the simulation's results. To obtain the expected size
spectrum with simulation we used the energy spectrum and the chemical composition ofprimary cosmic rays obtained by direct measurements and assumed the Leaky box model.
Those results are presented here.
THE PRINCIPLE OF OUR METHOD
The significant discrepancies were often found even in a size spectrum of Air shower.
Though the derivation of the size spectrum from observed data looks to be rather straightforward process, some systematic errors are not so easy to correct. Each experiment has its own
characteristics and systematic errors. This makes direct comparison of size spectrum of different
Air shower observations very difficult.
So we proposed one method with that the comparison would become possible.
First we assume the size of Air shower (the total number of electro-magnetic components)and shower transition does not depend much on their interaction model. If this assumption isreasonably true, we can calculate the Standardized Size spectrums for various depth from one
absolute primary energy spectrum. The comparison with such standard size spectrum will tell us
the amount of relative systematic errors in each observations. Unless we follow this kind ofmethod, reasonable error estimation among the observations is quite difficult. So the accuracyof the energy spectrum cannot be reduced.

EXPERIMENTAL CONDITIONS
The whole figure of our Ooty Air
shower array is shown in fig.1. 217
scintillation counters (each 1m2) areequally distributed with the distanceof 8 m over the area of 128 x 128 m.
The triggering condition was 9
detectors out of 90 should havegreater than 0.4 particles andtriggering rate was 12Hz under thiscondition. In the analysis of observed
data greater than 15 detectors areapplied to select the proper Air
shower.
So to accommodate this condition
for simulation, >0.4 particles in >15
detectors out of 90 detectors areadopted as a condition for picking up
the Air shower.
The accuracy of angle measurement
is around 2 degrees.

Figure 1:PROCESS OF ANALYSIS
1. We took the absolute primary cosmic rays (greater than 5 TeV) = 8.4 x 10-3 (/m2/sec/str)(Ichimura et. al.)The powers of energy spectrum is -2.7 < 2 x 1015eV and -3.15 > 2 x 1015 eV
Ratio of each nuclear group is Pr:He:CNO:SiMg:Fe = 0.4:0.3:0.1:0.05:0.15
2. We generate the Air shower from the minimum energy of 5 TeV. Since maximum shower
size generated from primary energy of 5 TeV is well under 104, the size spectrum derived
from this condition is free from distortion above 104.
3. The change of index of energy spectrum for proton is assumed at 2000 TeV
For other nuclei the change of index is proportional to atomic number (2000 x A)
4. Air shower is selected only θ smaller than sec θ <1.1 ( θ :zenith angle of AS.)

DISCUSSIONS AND CONCLUSIONS

Figure 2: Comparison between Observed
Size spectrum and simulation
As you can see from our results in figure 2, observed data and simulation showed excellent
agreement in the size region between 3 x 104 to 6 x 105 where our size estimation of observed
data is reliable.
Above 6 x 105 we found the systematic discrepancy in size estimation of observed data.
Below 4 x 104 there might be some rejection of Air shower due to strict selection criteria in ourdata analysis program. Since we have adopted the same energy spectrum as for Norikura
experiment (N.Ito et. Al.) to derive the size spectrum, I think validity of our present method andthe energy spectrum of primary cosmic rays are rather established.
For the next step we are planning to improve the analysis method in size estimation andaccommodate the all conditions which are adopted in data analysis into simulation. Then directcomparison between experiment and simulation can be performed.
Acknowledgements
We are grateful to the Ministry of education of Japan for their partial financial support for thisexperiment. The authors wish to thanks Prof.V.S.Narasimham and other member of the TIFROCU Proton Decay Collaboration for the loan of proportional counters used in the muondetector. We are also happy to acknowledge valuable contributions of N.V.Gopalakrishnan,G.Paul Francis, A.Peter, K.C.Ravindran, B.Sreenivasa Rao, S.Thirunavukkarasu,
K.Viswanathan and V.Viswanathan during the installation, operation and maintenance of theinstrumentation for the GRAPES III array. The help and cooperation of the Radio Astronomy
Center for providing site facilities for the GRAPES III array are gratefully acknowledged
REFERENCES
K.Kasahara and S.Torii Comput. Phys. Commun. 64, 109 (1991)
M.Ichimura et. Al. Phys. Rev. D, 48, 1949 (1993)
N.Ito et. Al. Proc. 25th ICRC Durban OG6.2.2 (1997)